Observable responses of micro-cantilever array to dynamic acoustic forces at higher mode in the broadband frequency window

We develop a theoretical framework describing numerical approach to explore dynamic acoustic force sensitivity using micro-cantilever array in monomodal and bimodal operations. The excitation force at the second eigenmode frequency is supplied to the micro-cantilevers in monomodal operation. Since we focus on measurement sensitivity of acoustic forces at higher frequencies, deflections of micro-cantilevers at higher mode, second flexural mode, are obtained. In bimodal operations, external driving forces at the first and second eigenmode frequencies are applied simultaneously for the actuation of micro-cantilevers in an array. Depending on acoustic force strength, the application of driving force at higher eigenmode frequency in bimodal excitation scheme increases the phase sensitivity in measurement of acoustic forces within a particular frequency scope. For both excitation schemes, oscillation observables such as amplitude and phase shift are determined with respect to acoustic force frequencies for diverse acoustic force strengths. Simulation results suggest that wider high-sensitivity frequency band could be acquired, utilizing resonantly excited micro-cantilever array. For our case, we obtain the high-sensitivity frequency band of around 200-270 kHz and 440-570 kHz for the acoustic force strengths in the range of 126-1138.5 pN.